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### April 28, 2016

**Exam #3:**

**Graded exams on Tuesday!**

**Graded exams on Tuesday!**

**Final Exam**

**Tuesday, May 10**

**Tuesday, May 10**

**th**_{, 10:30 a.m.}

_{, 10:30 a.m.}

**Room: Votey 207 **

**(tentative)****Review Session:**

**Sunday, May 8**

**th**

_{, 4 pm, Kalkin 325 }

_{, 4 pm, Kalkin 325 }

_{(tentative)}**Office Hours – Next week:**

**Office Hours – Next week:**

**moved to Wednesday, May 4**

**moved to Wednesday, May 4**

**th**_{, 2:00-3:30 pm}

_{, 2:00-3:30 pm}**Nuclear Magnetic **

**Resonance (NMR) **

**Spectroscopy**

### Chem 221

**Instrumental Analysis**

### Spring 2016

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### Overview

*Based on the interaction of RF EMR (up to ~1000 *
MHz) with matter (in a magnetic field)

*-EMR interactions with spin states of nuclei*
*-RF EMR: much lower energy than optical EMR*
First demonstrated in 1946

First commercial instrument: 1956 We will be concerned with:

origin of RF EMR interactions

how these interactions are measured

how chemical information can be obtained from NMR measurements

### Theory: Quantum Treatment

Energies of nuclear spin states are quantized:

* Nuclear Spin Quantum Number (I)*
where I = 0, ½, 1, 1½, etc.

**Three Groups of Nuclei:**
**1.** **I=0**

*-non-spinning nuclei, no magnetic moment, even # p*+_{& n}o
-examples: 12_{C, }16_{O}

**2.** **I=½**

-spherical spinning charge with magnetic moment
-examples: 13_{C, }1_{H}

**3.** **I>½**

*-non-spherical spinning charge with magnetic moment*
-examples: 2_{H, }14_{N}

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### More Quantum Numbers

*All nuclear spin states are degenerate unless in *

### a uniform magnetic field

**Where they split into 2I + 1 states**

*Defined by Magnetic Quantum Numbers (m):*

**m = I, I-1, I-2 . . . . -I**

**So, for I=0: m = 0 (only 1 state) NMR inactive****for I=½: m = ±½ (2 states) NMR ACTIVE**

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### Energy States

### For an I=½ system:

**E**

No MagField MagField

m = -½

m = +½

### ∆

**E = 2µ**

### β

**B**

_{o}**Particle magnetic moment: **

2.7927 nuclear magnetons
(for 1_{H)}

**Nuclear Magneton:**

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### In General:

Selection Rule:

### ∆

**m = ±1***For any value of I:*

**h**

### ν

**= (µ**

### β

**B**

_{o}

_{o}

**)/I**

•So, ν will vary with applied field strength (B_{o})
•Example: for 1_{H, }_{ν} _{= 60 MHz @ B}

o= 14,092 Gauss

### A Classical

### Perspective

A“classical” view will help us understand the

measurement process.

Consider a spinning charged
particle in a magnetic field:
•Particle will precess at a
characteristic frequency
*(Larmor Frequency) *

### ν

**:**

_{o}### ν

_{o}**= **

### γ

**B**

_{o}**/2**

### π

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### “Classical” view of

### Absorption

*Application of another magnetic field (B*_{1}**) perpendicular **

**to B _{o}** and at a frequency = ν

_{o}results in:

Absorption of applied EMR

Spin flip of particle to excited state

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### Instrumental

**Continuous Wave (CW) NMR**

original instruments used:
Electromagnets (14 - 23 kG; 60 - 100 MHz) Fixed frequency RF source

Swept (variable) magnetic field
*-measure absorption of applied RF*

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### Back to Boltzmann!

Using Boltzmann statistics, we can determine the relative populations of each of the two spin states:

**N**

_{2}

_{2}

**/N**

_{1}

_{1}

**= e**

**-**

### ∆

**E/kT**

•∆E is very small (relative to optical EMR) for RF EMR
•As ∆E ↓, N_{2}/N_{1} →1 (so, N_{2}≈ N_{1})

•BUT: for absorbance, we want N_{1} >> N_{2}

•If absorption rate > decay rate, not much absorbance can
occur before N_{1} = N_{2} (saturation)

•When transition is saturated, NO MORE ABSORPTION!

### Decay (relaxation) Processes

Two decay routes (non-radiative):

**1. Spin-Lattice Relaxation (T _{1})**

*-also called: longitudinal relaxation*

-due to interactions between nuclear spin states
**and magnetic micro environments in the sample ****-magnetic micro environments must be at the **

**Larmor Frequency of the absorbing nuclei in **

order to couple

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### Coupling Efficiency: T

_{1}

T_{1}*is the excited state lifetime associated with *
* spin-lattice relaxation (it is inversely proportional to the *
extent of spin-lattice relaxation)

**Temperature effects**

-at some temperature, the frequency of molecular
motion matches the Larmor frequency for a nucleus and
*coupling efficiency is at a maximum (T _{1}*

*is at a minimum)*

*-any change in temperature will result in an increase in*T

_{1}(decreased coupling efficiency)

*Any (e.g., viscosity) changes in lattice mobility will have a *
similar effect

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### More on T

_{1 }

### Processes

*Other lattice components that can reduce T*

_{1}

### :

unpaired electrons (from radicals and paramagnetic
species, like O_{2})

nuclei with I ≥1

### Efficient Spin-Lattice Relaxation results in:

Decreased likelihood of saturation Larger absorption signal (CW NMR) Other effects?

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### Spin-Spin Relaxation: T

_{2}

**Energy transfer with other magnetic nuclei**

Nuclei must be in close proximity

*Very efficient coupling in solids (T*_{2} ~ 10-4_{sec)}

*Has no effect on saturation*
**Will cause line broadening:**

∆ν= (2π∆t)-1 _{(according to Heisenberg)}

so: linewidth ∝1/T_{2}

(T2 ≈10-4sec → ∆ν ≈103Hz)

In solutions: (<1 sec)

**T**

_{2}### <

**T**

**(1-10 sec) Controls linewidths (~1 Hz)**

_{1}_{Affects saturation}

### How can S/N be increased?

**Increase B**

_{o}

-increases ∆E, increasing population difference
*between spin states, so more nuclei can undergo *
*transitions*

**-How? Superconducting Magnets**

**Multiplex Signal Measurement**

-small signal makes measurement limited by detector
*noise, so a multiplex measurement method should *
improve S/N

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### Pulsed FT-NMR

### At fixed B

_{o}

*, irradiate sample with a range*

**of RF EMR frequencies . . . How?**

**of RF EMR frequencies . . . How?**

*-by pulsing a fixed frequency (*ν_{o}) RF source, a
*range (*∆ν) of RF frequencies is generated.
-the extent of the range is determined by the
*pulse width:*

### ∆ν

### = 1/4

### τ

(according to Heisenberg) where:### τ

is the pulse width (seconds)18

### The Pulsed FT-NMR

### Measurement

RF Excitation Pulse Free Induction Decay19

### FT-NMR:

### Obtaining a Spectrum

Obtain maximum number of excited nuclei during the RF pulse (saturation)

*Measure RF Emission (signal generated by nuclei *
spin flips back to ground state) when RF source is
**off - FID**

**FID contains emission from all excited nuclei all at **

*their characteristic (Larmor) frequencies*
*Use Fourier Transform to convert time domain*
**FID to frequency domain spectrum**